Q: A block of mass $$m$$ slides down a rough incline of height $$h$$ and length $$L. If $$the coefficient of kinetic friction is $$\mu_k$$, what is the work done by friction?

$$W_f = -\mu_k m g \cos\theta \cdot L$$

Question 1

A person with mass $$m = 60\ \mathrm{kg}$$ weighs $$660\ \mathrm{N} on $$Earth. What is the acceleration due to gravity $$g on $$Earth based on this information?

Accepted Answer

$$g = 9.8\ \mathrm{m/s^2$}$$

Question 2

A person with mass $$m = 60\ \mathrm{kg}$$ weighs $$1744\ \mathrm{N} on $$Jupiter. What is the acceleration due to gravity $$g on $$Jupiter?

Accepted Answer

$$g = 14.7\ \mathrm{m/s^2$}$$

Question 3

A skier starts from rest and accelerates down a slope. If the net force acting on the skier is $$F_{net} = 300\ \mathrm{N}$$ and the mass is $$m = 71\ \mathrm{kg}$$, what is the acceleration $$a$$?

Accepted Answer

$$a = 4.2\ \mathrm{m/s^2$}$$

Question 4

A block of mass $$m is $$pulled across a horizontal surface with a coefficient of kinetic friction $$\mu_k = 0.4. If $$the normal force is $$N = 120\ \mathrm{N}$$, what is the frictional force $$f_k$$?

Accepted Answer

$$f_k = 48\ \mathrm{N}$$

Question 5

A block is attached to a spring with spring constant $$k = 2000\ \mathrm{N/m}$$ and is compressed by $$x = 0.06\ \mathrm{m}. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = 7.2\ \mathrm{J}$$

Question 6

A vector $$\vec{A}$$ has magnitude $$6.50$$ and a vector $$\vec{B}$$ has magnitude $$10.2. $$The angle between them is $$37.0^\circ. $$What is the scalar product $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$252.9$$

Question 7

If $$\vec{A}$$ and $$\vec{B}$$ are vectors with magnitudes $$6.50$$ and $$10.2$$ respectively, and the angle between them is $$37.0^\circ$$, what is the scalar product $$\vec{A} \cdot (-\vec{B})$$?

Accepted Answer

$$-252.9$$

Question 8

A person climbs a staircase of height $$h = 1.0\ \mathrm{m} in$$ $$1.0\ \mathrm{s}$$, with mass $$m = 70\ \mathrm{kg}. $$What is the power output if the work done is $$W = mgh$$?

Accepted Answer

$$P = 686\ \mathrm{W}$$

Question 9

A block slides down a frictionless incline of height $$h = 2.0\ \mathrm{m}. $$What is its speed at the bottom if it starts from rest?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 10

A block of mass $$m = 5.0\ \mathrm{kg} is $$pulled with a force $$F = 20\ \mathrm{N} on a $$horizontal surface with friction coefficient $$\mu_k = 0.2. $$What is the acceleration of the block?

Accepted Answer

$$a = 1.6\ \mathrm{m/s^2$}$$

Question 11

A block is compressed against a spring and released. If the spring constant is $$k = 2000\ \mathrm{N/m}$$ and the block is compressed $$x = 0.05\ \mathrm{m}$$, what is the maximum speed $$v of $$the block if its mass is $$m = 2.0\ \mathrm{kg}$$?

Accepted Answer

$$v = 2.24\ \mathrm{m/s}$$

Question 12

A person climbs $$10$$ steps, each of height $$h = 0.2\ \mathrm{m}$$, with mass $$m = 70\ \mathrm{kg}. $$What is the total work done against gravity?

Accepted Answer

$$W = 1372\ \mathrm{J}$$

Question 13

A block of mass $$m$$ slides down a rough incline of height $$h$$ and length $$L. If $$the coefficient of kinetic friction is $$\mu_k$$, what is the work done by friction?

Accepted Answer

$$W_f = -\mu_k m g \cos	heta \cdot L$$

Question 14

A block of mass $$m = 2.0\ \mathrm{kg} is $$compressed against a spring ($$k = 2000\ \mathrm{N/m}$$, $$x = 0.04\ \mathrm{m}) $$and released. What is the kinetic energy at the equilibrium position?

Accepted Answer

$$KE = 3.2\ \mathrm{J}$$

Question 15

A block of mass $$m is $$pulled at constant velocity across a horizontal surface. If the coefficient of kinetic friction is $$\mu_k$$ and the normal force is $$N$$, what is the pulling force $$F$$?

Accepted Answer

$$F = \mu_k N$$

Question 16

A block of mass $$m = 3.0\ \mathrm{kg} is $$pulled with a force $$F = 15\ \mathrm{N} on a $$surface with $$\mu_k = 0.3. $$What is the acceleration?

Accepted Answer

$$a = 1.5\ \mathrm{m/s^2$}$$

Question 17

A block of mass $$m is $$released from height $$h$$ and lands with speed $$v. $$Which equation relates $$v to$$ $$h$$?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 18

A person of mass $$m = 70\ \mathrm{kg}$$ climbs a vertical ladder of height $$h = 2.0\ \mathrm{m} in$$ $$2.0\ \mathrm{s}. $$What is the average power output?

Accepted Answer

$$P = 343\ \mathrm{W}$$

Physics Problem-Solving Guidance: Forces, Work, and Scalar Products

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