Q: A mercury pressure gauge is connected to a tank of gas as shown. What is the pressure of the gas if the height difference is $$0.18 \ \mathrm{m}$$?

$$2.36 \times 10^4$ \ \mathrm{Pa}$$

Question 1

A car starts from rest and accelerates uniformly at $$2.0 \ \mathrm{m/s^2$}$$ for $$5.0 \ \mathrm{s}. $$What is the car's final speed?

Accepted Answer

$$10.0 \ \mathrm{m/s}$$

Question 2

A block of mass $$2.0 \ \mathrm{kg} is $$sliding down a frictionless ramp inclined at $$30^\circ. $$What is the magnitude of the acceleration of the block?

Accepted Answer

$$4.9 \ \mathrm{m/s^2$}$$

Question 3

A $$15 \ \mathrm{N}$$ ball is thrown straight up with an initial speed of $$14 \ \mathrm{m/s}. $$What is the force due to gravity acting on the ball at its highest point?

Accepted Answer

$$15 \ \mathrm{N}$$

Question 4

A frog is sitting at rest on a slope. The angle of the slope is $$	heta. If $$the coefficient of static friction is $$\mu_s$$, what is the minimum value of $$\mu_s so $$the frog does not slide down?

Accepted Answer

$$\mu_s = 	an 	heta$$

Question 5

A spherical object with a diameter of $$2 \ \mathrm{cm} is $$moving through a fluid with a density of $$2200 \ \mathrm{kg/m^3$} at $$terminal speed. What is the magnitude of the drag force if the drag is purely resistive?

Accepted Answer

$$1.1 \ \mathrm{N}$$

Question 6

A $$3.0 \ \mathrm{kg}$$ mass is attached to a light spring fixed at one end, causing it to rotate in a circle of radius $$2.0 \ \mathrm{m} at a $$speed of $$5.0 \ \mathrm{m/s}. $$What is the spring's restoring force?

Accepted Answer

$$37.5 \ \mathrm{N}$$

Question 7

A block of mass $$m$$ slides up a frictionless ramp and compresses a spring by a distance $$d. If $$the block starts with speed $$v_0$$, what is the maximum compression of the spring?

Accepted Answer

$$d = \frac{m v_0$^2}{2 k}$$

Question 8

A $$10 \ \mathrm{kg}$$ box is pulled by a horizontal force over a horizontal surface with $$\mu_k = 0.2. $$What is the magnitude of the friction force?

Accepted Answer

$$19.6 \ \mathrm{N}$$

Question 9

A rod of length $$L is $$fixed horizontally at one end. If the bending coefficient is $$\beta$$ and the cross-sectional radius is $$r$$, what is the bending coefficient of a rod made from a similar material, but with twice the length and half the radius?

Accepted Answer

$$\frac{\beta}{16}$$

Question 10

A car is driving along a flat road at speed $$v. $$What is the speed that halves the kinetic energy of the car?

Accepted Answer

$$\frac{v}{\sqrt{2}}$$

Question 11

A $$1.0 \ \mathrm{kg}$$ block is initially at rest. A constant force does $$5.0 \ \mathrm{J} of $$work on the block as it slides up a ramp. What is the block's final speed?

Accepted Answer

$$3.2 \ \mathrm{m/s}$$

Question 12

A spring is totally compressed from the equilibrium position by a distance of $$0.5 \ \mathrm{m}. $$What is its new potential energy if $$k = 8 \ \mathrm{N/m}$$?

Accepted Answer

$$1.0 \ \mathrm{J}$$

Question 13

A $$0.07 \ \mathrm{m}$$ container has $$6000$$ molecules of salt. A membrane of $$0.001 \ \mathrm{m}$$ thickness is connecting this container to an outside water solution. The diffusion coefficient of salt is $$1.3 	imes 10$$^{-9}$$ \ \mathrm{m^2$/s}. $$What is the magnitude of the initial flux through the membrane in units of $$\mathrm{molecules}/\mathrm{m}^2\mathrm{s}$$?

Accepted Answer

$$8.6 	imes 10^6$

Question 14

A scientist measures the random motion of $$123$$ identical particles in a long tube. If $$0.08 of $$the particles have a displacement of $$0.24 \ \mu\mathrm{m}$$, how many particles would be expected to have this displacement?

Accepted Answer

$$9.84$$

Question 15

A mercury pressure gauge is connected to a tank of gas as shown. What is the pressure of the gas if the height difference is $$0.18 \ \mathrm{m}$$?

Accepted Answer

$$2.36 	imes 10^4$ \ \mathrm{Pa}$$

Question 16

A $$2.0 \ \mathrm{kg}$$ block is being pulled by a horizontal force $$F$$ over a surface with $$\mu_k = 0.3. $$What is the minimum force required to keep the block moving at constant velocity?

Accepted Answer

$$5.88 \ \mathrm{N}$$

Question 17

A $$0.5 \ \mathrm{kg}$$ mass is attached to a spring with $$k = 20 \ \mathrm{N/m}$$ and oscillates with amplitude $$0.1 \ \mathrm{m}. $$What is the maximum speed of the mass?

Accepted Answer

$$0.63 \ \mathrm{m/s}$$

Question 18

A $$1.0 \ \mathrm{kg}$$ block is launched from rest up a ramp with $$K = 1200 \ \mathrm{N/m}$$ and compresses the spring by $$0.2 \ \mathrm{m}. $$What is the initial speed of the block?

Accepted Answer

$$6.93 \ \mathrm{m/s}$$

Physics 131: Core Concepts and Problem-Solving in Mechanics and Fluids

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