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In this lesson, we will learn how to calculate the change in the momentum of an object that experiences a given force for a given time.

Q1:

Water from a fire hose is directed horizontally against a wall at a rate of 50.0 kg/s and a speed of 42.0 m/s. Calculate the force exerted on the wall, assuming the water’s horizontal momentum is reduced to zero.

Q2:

A car crashes into a large tree that does not move. The car decelerates from a velocity of 30 m/s to rest over a distance of 1.3 m. A driver of mass 70 kg is sitting in the car when it crashes.

What impulse is applied to the driver by the seatbelt, assuming he follows the same motion as the car?

What is the average force applied to the driver by the seatbelt?

Q3:

A piece of microdebris in Earth’s orbit has a mass of 8.55 µg. The debris strikes a spacecraft at a velocity of 1.28 km/s relative to the spacecraft. The microdebris particle comes to rest relative to the spacecraft 74.8 ns after striking it. What magnitude force was exerted on the spacecraft by the collision?

Q4:

A 65.0-kg-mass person jumps from the first floor window of a burning building and lands almost vertically on the ground with a horizontal velocity of 3.00 m/s and vertical velocity of − 9 . 0 0 m/s. Upon impact with the ground he is brought to rest in a short time. The force experienced by his feet depends on whether he keeps his knees stiff or bends them.

Find the magnitude of the impulse on the person from the impact on the ground.

Find the direction from the horizontal of the impulse on the person from the impact on the ground.

Find the average horizontal force on the person’s feet if the person keeps his legs stiff and straight and his center of mass drops by only 1.00 cm vertically and 1.00 cm horizontally during the impact.

Find the average vertical force on the person’s feet if the person keeps his legs stiff and straight and his center of mass drops by only 1.00 cm vertically and 1.00 cm horizontally during the impact.

Find the average horizontal force on the person’s feet if the person bends his legs throughout the impact so that his center of mass drops by 50.0 cm vertically and 5.00 cm horizontally during the impact.

Find the average vertical force on the person's feet if the person bends his legs throughout the impact so that his center of mass drops by 50.0 cm vertically and 5.00 cm horizontally during the impact.

Q5:

A bullet of mass 0.200 kg travels horizontally with a speed of 400 m/s. The bullet strikes a block of mass 1.50 kg that is initially at rest on a frictionless table, as shown.

After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit.

What is the magnitude of the velocity of the block/bullet combination immediately after the impact?

What is the magnitude of the impulse from the block on the bullet?

What is the magnitude of the impulse from the bullet on the block?

If the bullet’s deceleration to its final speed takes 3.00 ms, what average force is exerted by the block on the bullet during that time?

Q6:

An unwary football player collides with a padded goalpost while running at a velocity of 4.75 m/s and comes to a full stop after compressing the padding and his body by 0.244 m.

What is his acceleration?

How long does the collision last?

Q7:

A rugby player of mass 105 kg is moving at 6.45 m/s and collides with a padded goalpost. The collision exerts a force on the rugby player in the opposite direction to his motion of 15.0 kN for 72.8 ms. At what speed does the rugby player move away from the goalpost?

Q8:

A hammer of mass 0.385 kg moving horizontally at a speed of 5.75 m/s strikes a negligible mass nail sticking out horizontally from a wooden board. The hammer comes to rest when the nail is driven 120 mm into the board. During the contact between the nail and the hammer, they accelerate together as a single object.

How much time are the hammer and nail in contact before the hammer comes to rest?

Find the magnitude of the average force that the hammer exerts on the nail.

Q9:

The 𝑥 -component of the force applied on a golf ball of mass 38 g by a golf club is shown in the diagram.

What is the 𝑥 -component of the impulse applied on the golf ball between 0 ms and 50 ms?

What is the 𝑥 -component of the impulse applied on the golf ball between 50 ms and 100 ms?

Q10:

Approximately 5 0 0 0 0 years ago, a large iron-nickel meteorite collided with Earth, producing a crater 1 2 0 0 m in diameter, 170 m in depth, and with 45 m high walls. The meteorite before the strike can be modeled as a sphere of radius 25.00 m and density 7 9 7 0 kg/m^{3}. It collided with Earth at a speed of 1 . 2 8 × 1 0 4 m/s and came to rest in a time interval of 2.00 s.

What is the magnitude of the average force applied to Earth by the meteorite impact?

Find the magnitude of the maximum force applied to Earth by the meteorite impact, assuming that 𝐹 ( 𝑡 ) = 𝐹 𝑒 m a x − 𝑡 2 2 𝜏 2 , where 𝜏 = 1 𝑒 𝑡 m a x .

Q11:

A car moving at a speed of 27.0 m/s collides with a building, coming to rest in 1.00 s. The car’s driver has a weight of 860 N and is protected by both a seat belt and airbags that extend the time interval over which the driver comes to rest to 2.50 s.

What is the magnitude of the average force on the driver during his deceleration?

What would have been the magnitude of the average force on the driver during his deceleration without seat belt or airbags, assuming that the time interval for the driver to come to rest under these conditions would be 0.200 s?

Q12:

A fictional starship that has a mass of 2 . 0 × 1 0 9 kg accelerates from rest to a speed of 0 . 7 5 × 1 0 8 m/s in a time interval of 60 s.

What is the average force applied to the starship?

Accelerating at 98 m/s^{2}, how much time would be needed for the starship to reach a speed of 0 . 7 5 × 1 0 8 m/s?

Q13:

A mobile phone with a mass of 0.172 kg is dropped from a height of 1.5 m. The phone decelerates from the speed it gained by falling to rest in a time interval of 0.026 s.

What is the magnitude of the average force exerted on the phone by the ground?

What is the magnitude of the average force exerted on the phone by the ground if, rather than coming to rest, the phone rebounds from the ground, initially moving at a speed negligibly less than the speed at which it hit the ground?

Q14:

During the 2007 French Open, Venus Williams made the fastest recorded serve in a premier women’s tennis match. The ball’s speed was 58 m/s. What average force would need to be applied to a ball of mass 0.057 kg over a 5.0 ms time interval to accelerate it from rest to a speed of 58 m/s? Ignore any speed that the ball gains due to acceleration by gravity.

Q15:

In a physics laboratory, two carts move on a track that produces negligible friction. The carts’ ends contain magnets so that the carts stick together if their ends contact each other. One cart has a mass of 0.675 kg and moves to the right at 0.750 m/s, while the other has a mass of 0.500 kg and moves to the right at 1.33 m/s, catching up with the first cart and colliding with it.

What is the speed of the carts after they collide?

The collision is repeated, this time with the 0.500 kg mass cart moving to the left. What is the velocity of the carts after they collide? Assume that motion to the right corresponds to positive velocity.

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