Question

modified true/false indicate whether the statement is true or false. if false, change the underlined part of sentence to make the statement true. 2 marks - k/u1. the acceleration due to gravity increases as two objects get farther from each other2. two objects in a system will always have the same tension between them.multiple choice circle the choice that best completes the statement or answers the question. 8 marks - k/u3. which of the following scenarios must be true about an object experiencing zero net force?a. the frictional force must be zerob. the objects acceleration must be zeroc. the object can be speeding up or slowing downd. the object must be at reste. none of the above4. in which of the following scenarios is the frictional force kinetic?a. a soccer ball rolling down a hillb. a person leaning against a wall while standing stillc. a person turning a door knobd. a car driving on the highway without slippinge. none of the above5. select the choice to make a true statement: the force of gravity between two objects is...a. proportional to ( r^{2} )b. inversely proportional to ( r^{2} )c. proportional to ( r )d. inversely proportional to ( r )e. none of the above6. two identical books a and b are pushed with horizontal forces along a rough table top. both books travel at constant velocities, but as velocity is twice as fast as bs velocity. which statement is true?a. the net force on a is the same as the net force on bb. the applied force on a is double the applied force on bc. the coefficient of friction between the table and book a is double the coefficient of friction between the table and book bd. the frictional force acting on a is double the frictional force acting on b.e. none of the above7. a 32 kg child sits in a 13 kg sled. if the coefficient of static friction between the sled and the snow is 0.48, how much force is needed to start moving the sled?a. 210 nb. 61 nc. 22 nd. 150 ne. none of the above

Explanation:

Step1: Analyze question 3

According to Newton's second law \(F = ma\), if the net force \(F = 0\), then \(a=\frac{F}{m}=0\). Frictional force is not necessarily zero (e.g., when there are other forces balancing it). An object with zero net force has constant velocity (can be moving at a constant speed, not necessarily at rest and not speeding up or slowing down).

Step2: Analyze question 4

Kinetic friction acts when there is relative motion between two surfaces. A soccer ball rolling down a hill has kinetic friction (rolling is a form of relative motion). A person leaning against a wall has static friction (no relative motion). A person turning a door knob - the knob is in rotational motion but the force here is more about torque and static friction in some aspects (no sliding). A car driving without slipping has static friction (the contact point of the tire with the road has no relative motion at the instant of contact).

Step3: Analyze question 5

The formula for gravitational force is \(F=\frac{Gm_1m_2}{r^{2}}\), so it is inversely proportional to \(r^{2}\).

Step4: Analyze question 6

Since both books are moving at constant velocity, by Newton's first law, the net force on each book is \(F_{net}=0\) (because \(a = 0\)). The frictional force \(F_f=\mu N\), and since the books are identical (\(N = mg\) same) and on the same table (\(\mu\) same), \(F_f\) is same. The applied force \(F_{applied}=F_f\) (because \(F_{net}=F_{applied}-F_f = 0\)), so applied forces are same.

Step5: Analyze question 7

The normal force \(N=(m_{child}+m_{sled})g=(32 + 13)\times9.8=440.2N\). The maximum static frictional force \(F_{s,max}=\mu_sN\). Substituting \(\mu_s = 0.48\) and \(N = 440.2N\), we get \(F_{s,max}=0.48\times440.2\approx211.3N\approx210N\)

Answer:

1. b. the object's acceleration must be zero
2. a. A soccer ball rolling down a hill
3. b. Inversely proportional to \(r^{2}\)
4. a. The net force on A is the same as the net force on B
5. a. \(210N\)