Worksheet: Mechanical Energy and Dynamics

In this worksheet, we will practice applying the principle of the conservation of energy to systems involving kinematics, resistive forces, and other variable forces.

Q1:

A boy throws a ball of mass 0.25 kg vertically upward with an initial speed of 20 m/s. The ball moves vertically upward, comes instantaneously to rest, and then accelerates vertically downward and returns to the point from which it was thrown. When the ball returns to its original position, its speed is 17 m/s. How much work was done by air resistance on the ball during its flight?

Q2:

A crate of mass 50 kg is being pushed across a rough surface at a steady 8.0 m/s. The crate is then released and comes to a stop in 10 seconds. What is the average rate at which the frictional force on the crate removes kinetic energy from it?

Q3:

An 80.0 kg sprinter accelerates from rest to 12.0 m/s in 2.90 s.

What is the average power output of the sprinter in watts?

What is the average power output of the sprinter in horsepower? In metric horsepower, 1 hp = 735.5 W.

Q4:

A boy pulls a 5.00-kg cart with a 20.0-N force at an angle of 30.0∘ above the horizontal for a length of time. Over this time, the cart moves a distance of 12.0 m on the horizontal floor.

Find the work done on the cart by the boy.

What will be the work done by the boy if he pulled with the same force horizontally instead of at an angle of 30.0∘ above the horizontal over the same distance?

Q5:

A baseball of mass 0.25 kg is hit at the home plate with a speed of 40 m/s. The baseball lands in a seat in the left-field bleachers, a 120-m-horizontal distance and 20-m-vertically upward distance from the home plate. The baseball has a speed of 30 m/s when it lands. How much work is done on the ball by air resistance?

Q6:

A hockey puck of mass 0.17 kg is shot across a rough floor where the roughness varies at different locations. The variation in roughness of the floor can be described by a position-dependent coefficient of kinetic friction between the puck and the floor. For a puck moving along the 𝑥-axis, the coefficient of kinetic friction is given by 𝜇(𝑥)=0.10+0.050𝑥, where 𝑥 is in m.

Find the work done by frictional force on the hockey puck between 𝑥=0.0m and 𝑥=2.0m.

Find the work done by frictional force on the hockey puck between 𝑥=2.0m and 𝑥=4.0m.

Q7:

Engineers desire to model the magnitude of the elastic force of a bungee cord using the equation 𝐹(𝑥)=𝑎𝑥+9.009.00−9.00𝑥+9.00,mmmm

where 𝑥 is the stretch of the cord along its length and 𝑎 is a constant. If it takes 22.0 kJ of work to stretch the cord by 16.7 m, determine the value of the constant 𝑎.

Q8:

A box has a mass of 2.78 kg. The box accelerates by 3.76 m/s2 when it is pulled across a horizontal distance of 16.2 cm by a horizontally applied force. The surface has a coefficient of friction of 0.445 with the box. Assume that the direction of the boxes motion corresponds to positive displacement.

Find the work done on the box by the applied force.

Find the work done on the box by frictional force.

Find the work done on the box by the net force that acts on it.

How much does the kinetic energy of the box change due to the forces applied to it?

Q9:

A 74.3-kg-mass passenger in an SUV traveling at 91.4 km/h is wearing a seat belt. Suddenly, the driver slams on the brakes and the SUV stops. The SUV moves 51.4 m between the breaks being applied and coming to rest. Find the force exerted by the seat belt on the passenger.

Q10:

An elevator cable lifts an elevator with an acceleration of 0.800 m/s2 against a frictional force of 200 N. The mass of the loaded elevator is 1,500 kg.

What must the force supplied by the elevator cable be?

  • A 9 . 9 9 × 1 0  N
  • B 1 . 6 1 × 1 0  N
  • C 2 . 3 1 × 1 0  N
  • D 1 . 7 4 × 1 0  N
  • E 1 . 8 4 × 1 0  N

How much work is done by the cable in lifting the elevator 20.0 m?

  • A 1 . 9 0 × 1 0  J
  • B 3 . 2 2 × 1 0  J
  • C 3 . 1 4 × 1 0  J
  • D 4 . 3 2 × 1 0  J
  • E 2 . 2 2 × 1 0  J

What is the final speed of the elevator if it starts from rest?

How much work went into thermal energy?

Q11:

A shot-putter accelerates a 7.27 kg shot from rest to 14.0 m/s in 1.20 s, lifting it 0.800 m as he does so.

Calculate the power output in watts of the shot-putter as he does this, excluding the power produced to accelerate his body.

Calculate the power output in metric horsepower of the shot-putter as he does this, excluding the power produced to accelerate his body. In metric horsepower, 1 hp = 735.5 W.

Q12:

In a downhill ski race, surprisingly, little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy on even small hills.

Consider a skier who skies 80.0 m down a 35.0∘ slope. Ignore any effects of friction.

Find the final speed if the skier starts at rest.

Find the time taken if the skier starts at rest.

Find the final speed if the skier starts with an initial speed of 2.50 m/s.

Find the time taken if the skier starts with an initial speed of 2.50 m/s.

Q13:

A 100 g toy car is propelled by a compressed spring that makes it start moving. The car moves up a curved track. What is the final speed of the toy car if its initial speed is 2.00 m/s and it coasts up the frictionless slope, gaining 0.180 m in altitude?

Q14:

An asteroid located 6.0×10 km from Earth’s surface has a mass of 1.5×10 kg. The asteroid moves directly toward Earth at a relative speed of 2.0 km/s on a collision course.

What will the asteroid’s speed relative to Earth be just before impacting its surface?

  • A 5 5 × 1 0  m/s
  • B 1 6 × 1 0  m/s
  • C 6 3 × 1 0  m/s
  • D 1 3 × 1 0  m/s
  • E 1 1 × 1 0  m/s

What will the kinetic energy of the asteroid be just before it hits the surface of Earth?

  • A 1 5 × 1 0   J
  • B 9 . 7 × 1 0   J
  • C 3 . 2 × 1 0   J
  • D 3 . 6 × 1 0   J
  • E 3 . 5 × 1 0   J

Q15:

A comet is observed at a distance of 6.50 AU from the center of the Sun, moving at a speed of 36.4 km/s. The comet has a mass of 1.00×10 kg. Find the total energy of the comet. Use a value of 1.496×10 m for one AU.

  • A − 2 . 3 6 × 1 0   J
  • B 5 . 2 6 × 1 0   J
  • C 2 . 3 6 × 1 0   J
  • D 0 . 2 3 × 1 0   J
  • E − 0 . 6 2 × 1 0   J

Q16:

A bullet has a mass of 2.60 g and moves horizontally at a speed of 335 m/s as it collides with a stack of eight pine boards, each 0.750 ft thick. The bullet decelerates as it penetrates the boards, and the bullet comes to rest just as it has moved the full distance through the thickness of all eight boards. Find the average force exerted by the boards on the bullet. Assume that the motion of the boards due to the bullet’s impact is negligible.

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