Worksheet: Normal Reaction Force

In this worksheet, we will practice calculating the forces exerted by surfaces in reaction to forces applied to them, such as on objects on inclined slopes.

Q1:

A roller coaster car starts to move from rest at the top of a track that is 30.0 m long and inclined at an angle 20.0 below the horizontal. Assume that friction is negligible.

What is the magnitude of the acceleration of the car?

How much time passes before the car reaches the bottom of the track?

Q2:

A block of mass 2.0 kg is on a perfectly smooth ramp that makes an angle of 30 below the horizontal.

What is the magnitude of the block’s acceleration down the ramp?

What is the magnitude of the force of the ramp on the block?

What magnitude force applied upward along and parallel to the ramp would allow the block to move with constant velocity?

Q3:

A 120 kg astronaut is riding in a rocket sled that is sliding along an inclined plane. The sled has a horizontal component of acceleration of 5.0 m/s2 and a downward component of 3.8 m/s2. Calculate the magnitude of the force on the rider by the sled. Remember that gravitational acceleration must be considered.

Q4:

A student’s backpack, full of textbooks, is hung from a spring scale attached to the ceiling of an elevator. When the elevator is accelerating downward at 3.8 m/s2, the scale reads 60 N.

What is the mass of the backpack?

What does the scale read if the elevator moves upward while slowing down at a rate 3.8 m/s2?

What does the scale read if the elevator moves upward at constant velocity?

If the elevator had no brakes and the cable supporting it were to break loose so that the elevator could fall freely, what would the spring scale read?

Q5:

A piano is pushed from rest upward along a frictionless ramp aligned 17.5 above the horizontal. The direction of the applied force is parallel to the ramp. The piano’s mass is 286 kg and the magnitude of the force pushing the piano is 1,245 N.

What is the magnitude of the piano’s acceleration along the ramp?

The ramp is 2.7 m long. What is the speed of the piano when it reaches the top of the ramp?

Q6:

A horizontal force is applied to a block that has a weight of 1.50 kN. The force holds the block at rest on a plane inclined at 30.0 degrees above the horizontal. Assuming no friction, calculate the horizontal force’s magnitude.

Q7:

A man with a mass of 75.0 kg measures his weight by standing on a bathroom scale. The man and the scale are inside an elevator that can move at different rates.

What is the measurement of the man’s weight according to the scale if the elevator is accelerating vertically upward at a rate of 1.20 m/s2?

What is the measurement of the man’s weight according to the scale if the elevator is moving vertically upward at a speed of 1.20 m/s?

What is the measurement of the man’s weight according to the scale if the elevator is accelerating vertically downward at a rate of 1.20 m/s2?

  • A677 N
  • B645 N
  • C735 N
  • D747 N
  • E723 N

Q8:

A man with a mass of 85 kg walks on a sawhorse, as shown in the diagram. The sawhorse is 2.2 m long, 1.0 m high, and 30.0 kg in mass. The man is 0.40 m from the far end of the sawhorse. The total reaction force on the sawhorse is the vector sum of two reaction forces that each acts along one pair of the sawhorse’s legs. The normal reaction force at the contact point of a sawhorse leg with the floor is the normal component of the total reaction force that acts normally to the ground.

What is the magnitude of the normal reaction force of each sawhorse leg at the contact point with the floor at the end of the sawhorse farthest from the man?

What is the magnitude of the normal reaction force of each sawhorse leg at the contact point with the floor at the end of the sawhorse nearest to the man?

Q9:

A physics professor pushes a cart of demonstration equipment to a lecture hall, as shown in the diagram. Her mass is 65 kg, the cart’s mass is 12 kg, and the equipment’s mass is 7.0 kg. The professor exerts a backward force of 150 N on the floor. Calculate the force the professor exerts on the cart if it accelerates at 1.5 m/s2. All forces opposing the motion, such as friction on the cart’s wheels and air resistance, total 24 N.

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