Question

modified true/false indicate whether the statement is true or false. if false, change the identified word or phrase to make the statement true. (1-k each, 2-k total)

1. acceleration due to gravity can change depending on the altitude you are from earth
2. two objects in a system will always have the same acceleration.

multiple choice circle the choice that best completes the statement or answers the question. 8 marks - k/u

1. in which of the following scenarios could kinetic friction be beneficial for safety?

a. pulling a heavy box across the floor
b. pulling up in a car to a stop sign
c. tobogganing down a hill
d. turning a door knob
e. none of the above

1. identical books a and b are pushed with horizontal forces along a rough table top. both books travel at constant velocities, but as speed with double bs speed. which statement must be true?

a. the force of friction acting on a is double the force of friction acting on b
b. the applied force on a is double the applied force on b
c. the coefficient of friction between the table and book a is double the coefficient of friction between the table and book b
d. the net force on a is equal to the net force on b
e. none of the above

1. which of the following scenarios must be true about a non-zero net force?

a. the applied force must be zero
b. the force of friction must be zero
c. the object is moving at a constant velocity
d. the acceleration of the object is not zero
e. the direction of the applied force and the force of friction is the same

1. a 37.0 kg child sits on a light sled at rest. if the coefficient of static friction between the sled and the snow is 0.510, how much force is needed to start moving the sled and child?

a. 18.9 n c. 37.5 n e. none of the
b. 185 n d. 180 n above

1. select the choice to make a true statement: the force of gravity between two objects is...

a. inversely proportional to ( r^{2} )
b. proportional to ( r^{2} )
c. inversely proportional to ( r )
d. proportional to ( r )
e. none of the above

1. as you move further from the surface of the earth, the acceleration due to gravity would:

a. increase
b. decrease
c. remain unchanged
d. not enough information is provided

Explanation:

Step1: Analyze Question 3

Kinetic friction is beneficial when it helps in stopping or controlling motion. Pulling up a car to a stop sign relies on kinetic friction (between brake pads and discs etc.) to slow down and stop the car safely. Pulling a heavy box (a) - kinetic friction is a hindrance. Tobogganing down a hill (c) - kinetic friction slows but not for safety in a positive sense here. Turning a door knob (d) - static friction is more relevant.

Step2: Analyze Question 4

Since both books are moving at constant velocities, by Newton's first law, the net force \(F_{net}=ma\) (where \(a = 0\) for constant velocity). So, \(F_{net,A}=F_{net,B}=0\). The frictional force \(F_f=\mu N\), and since \(N = mg\) (same for A and B as identical books) and \(\mu\) (coefficient of friction) depends on the surfaces (same table - same \(\mu\)), \(F_f\) is same. Applied force \(F_{app}=F_f\) (because \(F_{net}=F_{app}-F_f = 0\)), so applied forces are same.

Step3: Analyze Question 5

By Newton's second law \(F_{net}=ma\). If \(F_{net}
eq0\), then \(a=\frac{F_{net}}{m}
eq0\) (since \(m>0\)). The applied force (a) doesn't have to be zero (\(F_{net}=F_{app}-F_f\)). Force of friction (b) can be non - zero. If \(F_{net}
eq0\), velocity is not constant (c). Applied force and friction (e) are usually in opposite directions.

Step4: Analyze Question 6

The force needed to start moving (overcome static friction) is \(F_{s,max}=\mu_s N\). \(N = mg\) (where \(m = 37.0\space kg\), \(g=9.8\space m/s^2\)). So \(N=37.0\times9.8 = 362.6\space N\). \(F_{s,max}=\mu_s N=0.510\times362.6\approx185\space N\)

Step5: Analyze Question 7

The gravitational force formula is \(F_g=\frac{Gm_1m_2}{r^2}\), so \(F_g\propto\frac{1}{r^2}\) (inversely proportional to \(r^{2}\))

Step6: Analyze Question 8

The formula for acceleration due to gravity \(g=\frac{GM}{r^{2}}\) (where \(M\) is the mass of the Earth, \(G\) is the gravitational constant, and \(r\) is the distance from the center of the Earth). As \(r\) (distance from the Earth's surface increases, \(r\) in the formula \(g=\frac{GM}{r^{2}}\) increases, so \(g\) decreases.

Answer:

1. b. pulling up in a car to a stop sign
2. d. the net force on A is equal to the net force on B
3. d. the acceleration of the object is not zero
4. b. \(185\space N\)
5. a. Inversely proportional to \(r^{2}\)
6. b. Decrease