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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