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In this lesson, we will learn how to apply Newton's laws of motion to systems involving nonnegligible resistive forces.

Q1:

A car is moving along a highway when the driver has to make an emergency stop. The wheels of the car lock and cease rolling. The car skids and leaves straight-line skid trails between the point where the braking began and the point where the car comes to rest. The skid trails are 27.9 m long. The coefficient of kinetic friction between the car’s tires and the road is 0.512. At what speed was the car moving when its wheels locked?

Q2:

A snow-boarder moves upward along a snowy slope inclined at 3 . 2 2 ∘ above the horizontal. The coefficient of kinetic friction with their board on the snow is 0.100. What is the magnitude of the snow-boarder’s deceleration?

Q3:

A motorcycle of mass 245 kg has an acceleration of 3.50 m/s^{2} while traveling at 90.00 km/h. The forces resisting the motorcycle’s motion, including friction and air resistance, total 400 N. What is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration?

Q4:

A sled of mass 15 kg moves across a horizontal surface that is covered in snow. The sled is pulled by a rope aligned at 2 3 ∘ above the horizontal. The coefficient of kinetic friction between sled and snow is 0.24.

The force supplied by the rope has a magnitude of 39 N.

What is the magnitude of the horizontal acceleration of the sled?

What magnitude force must the rope supply to pull the sled at constant velocity?

Q5:

A crate of mass 100 kg rests on a rough surface inclined at an angle of 3 7 ∘ with the horizontal. A massless rope to which a force can be applied parallel to the surface is attached to the crate and leads to the top of the incline. In this state, the crate is just ready to slip and start to move down the plane. The coefficient of friction is 8 0 % of that for the static case.

What is the coefficient of static friction?

What is the magnitude of the maximum force that can be applied upward along the plane on the rope and not move the block?

If a slightly greater force is applied, the block will slide up the plane. Once it begins to move, what is the magnitude of the acceleration necessary to keep the block moving upward at constant speed?

What is the magnitude of the reduced force necessary to keep the block moving upward at constant speed?

If the block is given a slight nudge to get it started down the plane, what will be the magnitude of its acceleration in that direction?

Once the block begins to slide downward, what magnitude of upward force on the rope is required to keep the block from accelerating downward?

Q6:

Consider the 65.0-kg ice skater being pushed by two others shown in the figure.

Remember that friction always acts in the direction opposite that of motion or attempted motion between surfaces in contact.

Find the direction and magnitude of ⃑ 𝐹 t o t the total force exerted on her by the others, given that the magnitudes ⃑ 𝐹 2 and ⃑ 𝐹 1 are 26.4 N and 18.6 N, respectively.

What is her initial acceleration if she is initially stationary and wearing steel-bladed skates that point in the direction of ⃑ 𝐹 t o t ?

What is her acceleration assuming she is already moving in the direction of ⃑ 𝐹 t o t ?

Q7:

A freight train consists of two engines and 38 cars. Each engine has a mass of 6 . 3 5 × 1 0 5 kg and the average mass of the cars is 3 . 4 4 × 1 0 5 kg. The force of friction of the track on the train’s wheels is 6 . 4 5 × 1 0 5 N. The train accelerates at 3 . 3 5 × 1 0 − 2 m/s. What is the magnitude of the force that the train exerts on the track?

Q8:

If half of the weight of a small utility truck with a mass of 1 . 0 0 × 1 0 3 kg is supported by its two drive wheels, what is the maximum magnitude of acceleration that the truck can achieve on dry concrete if the coefficient of static friction of the truck’s tyres on dry concrete is 1.0?

Q9:

A car that weighs 1 1 . 1 5 × 1 0 3 N accelerates from rest to a velocity of 76.0 km/h in 4.45 s. The car accelerates across a surface that exerts 1 2 2 5 N of friction force on the car’s wheels. What force does the car’s engine apply to the its wheels?

Q10:

A block is pushed upward along a slope inclined at 2 4 ∘ above the horizontal by a horizontally acting force of magnitude 175 N. The coefficient of kinetic friction between the block and the incline is 0.38. What is the magnitude of the acceleration of the block?

Q11:

A car is accelerating up a slope inclined at 5 . 1 0 ∘ above the horizontal. Half of the weight of the car is supported by its two drive wheels. The tyres do not slip during the acceleration. The coefficient of static friction for the car’s tyres on the slope is 0.700. What is the maximum magnitude of acceleration that the car can have?

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