Q: An object is being acted upon by three forces and moves with a constant velocity. One force is $$60 \\ \mathrm{N}$$ east, the second is $$75 \\ \mathrm{N}$$ along a direction making a counterclockwise angle of $$150^\\circ$$ with the first force. What is the magnitude and direction of the third force, measured clockwise from the x-axis?

$$75 \\ \mathrm{N}$$, $$330^\\circ$$

Q: A $$5.0 \\ \mathrm{kg}$$ box slides on the surface of a ramp that rises at $$37^\\circ$$ above the horizontal. The coefficient of kinetic friction between the box and the surface of the ramp is $$0.40. $$What are the magnitude and direction of the acceleration of the box if it is sliding up the ramp?

$$a = 2.5 \\ \mathrm{m/s^2$}$$, down the ramp

Question 1

An astronaut weighs 99 N on the Moon, where the acceleration due to gravity is $$1.62 \ \mathrm{m/s^2$}. $$How much does she weigh on Earth?

Accepted Answer

$$603 \ \mathrm{N}$$

Question 2

A block is on a frictionless table, on Earth. The block accelerates at $$5.3 \ \mathrm{m/s^2$}$$ when a $$10 \ \mathrm{N}$$ horizontal force is applied to it. The block and table are set up on the Moon where the acceleration due to gravity is $$1.62 \ \mathrm{m/s^2$}. A $$horizontal force of $$5 \ \mathrm{N} is $$now applied to the block when it is on the Moon. The force is applied tangent to the block by a thin cord. What is the acceleration of the block on the Moon?

Accepted Answer

$$2.65 \ \mathrm{m/s^2$}$$

Question 3

An object that weighs $$75 \ \mathrm{N} is $$pulled on a horizontal surface by a horizontal pull of $$50 \ \mathrm{N} to $$the right. The friction opposing this object is $$20 \ \mathrm{N}. $$What is the acceleration of the object?

Accepted Answer

$$2.1 \ \mathrm{m/s^2$}$$

Question 4

A $$50.0 \ \mathrm{kg}$$ crate is being pulled along a horizontal smooth surface. The pulling force is $$100 \ \mathrm{N} in a $$direction $$20^\circ$$ above the horizontal. What is the magnitude of the acceleration of the crate?

Accepted Answer

$$1.88 \ \mathrm{m/s^2$}$$

Question 5

An object is being acted upon by three forces and moves with a constant velocity. One force is $$60 \ \mathrm{N}$$ east, the second is $$75 \ \mathrm{N}$$ along a direction making a counterclockwise angle of $$150^\circ$$ with the first force. What is the magnitude and direction of the third force, measured clockwise from the x-axis?

Accepted Answer

$$75 \ \mathrm{N}$$, $$330^\circ$$

Question 6

A 10-kg picture is held in place by two wires, the first one hanging at $$60^\circ to $$the left of the vertical and the second one at $$45^\circ to $$the right of the vertical. What is the tension in the left wire?

Accepted Answer

$$69.8 \ \mathrm{N}$$

Question 7

A piano weighing $$1000 \ \mathrm{N} is $$lifted vertically at constant speed by a cable. What is the tension in the cable?

Accepted Answer

$$1000 \ \mathrm{N}$$

Question 8

Three blocks, light connecting ropes, and a light frictionless pulley compose a system. An external force of magnitude $$P is $$applied downward on block A, causing block A to accelerate downward at a constant $$2.5 \ \mathrm{m/s^2$}. $$The tension in the rope connecting block B and block C is equal to $$60 \ \mathrm{N}. $$What is the mass of block C?

Accepted Answer

$$24 \ \mathrm{kg}$$

Question 9

Two blocks are connected by a string over an ideal pulley as shown. Block A ($$5.0 \ \mathrm{kg}) is on a $$table, block B ($$10.0 \ \mathrm{kg}) $$hangs off the edge. What is the acceleration of the $$10.0 \ \mathrm{kg}$$ block when the other block is gently released?

Accepted Answer

$$3.85 \ \mathrm{m/s^2$}$$

Question 10

A $$5.0 \ \mathrm{kg}$$ box slides on the surface of a ramp that rises at $$37^\circ$$ above the horizontal. The coefficient of kinetic friction between the box and the surface of the ramp is $$0.40. $$What are the magnitude and direction of the acceleration of the box if it is sliding up the ramp?

Accepted Answer

$$a = 2.5 \ \mathrm{m/s^2$}$$, down the ramp

Question 11

A curved section of a horizontal highway is a circular unbanked arc of radius $$74.0 \ \mathrm{m}. If $$the coefficient of static friction between this roadway and typical tires is $$0.40$$, what would be the maximum safe driving speed for this highway curve?

Accepted Answer

$$15.2 \ \mathrm{m/s}$$

Question 12

A $$3.0 \ \mathrm{kg}$$ package is placed on a rough plane inclined at $$30^\circ$$ above the horizontal. The coefficient of static friction between package A and the plane is $$0.40. $$What minimum mass should package B have in order to start package A sliding up the ramp?

Accepted Answer

$$2.1 \ \mathrm{kg}$$

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