Question
Block A is placed on a rough surface inclined at an angle θ above the horizontal. A taut string connects block A over a pulley to block B, which hangs from the string, as shown below. The masses of blocks A and B are MA and MB, respectively. At time t=0, block A is sliding up the slope as block B falls, and the blocks are both slowing down. Assume that the mass and friction of the pulley are negligible.
If the mass of block B is 2kg, the gravitational force exerted on block B is most nearly which of the following?
A \(0.2N\)
B \(2N\)
C \(20N\)
D It is impossible to determine without knowing the mass of block A .
▶️Answer/Explanation
Ans:C
The gravitational force is the product of mass and the acceleration due to gravity. 2kg times 10N/kg gives a force of 20N.
Question
A 5kg object is released from rest near the surface of a planet such that its gravitational field is considered to be constant. The mass of the planet is unknown. After 2s, the object has fallen 30m. Air resistance is considered to be negligible. What is the gravitational force exerted on the 5kg object near the planet’s surface?
A \(5N\)
B \(15N\)
C \(37.5N\)
D \(75N\)
▶️Answer/Explanation
Ans:D
The kinematics equation that relates distance, time, and acceleration is used to calculate the acceleration of the object as it falls near the planet’s surface:
\(x=x_0+v_{x0}t+\frac{1}{2}a_xt^2\)
\(∴a=\frac{2x}{t^2}=\frac{2(7.5m)}{(1s)^2}=15 m/s^2\)
. Using the acceleration, the equation for weight can be used to calculate the weight of the 5 kg object: \(Σ\vec{F} =ma=(5kg)(15m/s^2)=75N\).
Question
A 5kg object is released from rest near the surface of a planet such that its gravitational field is considered to be constant. The mass of the planet is unknown. After 2s, the object has fallen 30m. Air resistance is considered to be negligible. What is the gravitational force exerted on the 5kg object near the planet’s surface?
A \(5N\)
B \(15N\)
C \(37.5N\)
D \(75N\)
▶️Answer/Explanation
Ans:D
The kinematics equation that relates distance, time, and acceleration is used to calculate the acceleration of the object as it falls near the planet’s surface:
\(x=x_0+v_{x0}t+\frac{1}{2}a_xt^2\)
\(∴a=\frac{2x}{t^2}=\frac{2(7.5m)}{(1s)^2}=15 m/s^2\)
. Using the acceleration, the equation for weight can be used to calculate the weight of the 5 kg object: \(Σ\vec{F} =ma=(5kg)(15m/s^2)=75N\).
Question
Ablock of mass M is attached to a modified Atwood machine and is accelerated upward at \(3a\) by a constant force \(F_0)
. What is the weight of the block?
A \(F_0−Mg\)
B \(3Mg\)
C \(2Mg\)
D \(Mg\)
▶️Answer/Explanation
Ans:D
Weight is a gravitational force exerted on a mass when it is within a gravitational field created by another mass. Weight can be calculated by \(F=Mg\) .
Question
The amusement park ride shown above takes riders straight up a tall tower and then releases an apparatus holding seats. This apparatus free-falls back to Earth and is stopped safely right above the ground. Which of the following indicates the magnitude of the gravitational force exerted on a rider of mass m on the way up and on the way down?
▶️Answer/Explanation
Ans:C
The gravitational force on an object near the surface of Earth always has magnitude \(mg\).
Question
Identical spheres are dropped from a height of 100m above the surfaces of both Planet X and Planet Y. The position of the spheres as a function of time is recorded as the spheres fall. These data are shown in the graphs above. Which planet exerts a greater gravitational force on the sphere, and what evidence supports this conclusion?
A Planet X , because the object’s final speed is greater.
B Planet X , because the object’s time of fall is greater.
C Planet Y , because the area under the curve is smaller.
D Planet Y , because the magnitude of the slope of the curve increases at a faster rate.
▶️Answer/Explanation
Ans:D
If a planet exerts a greater force due to gravity, then the acceleration due to gravity of an object would be greater. \(F_{gravity}=mg\) . This greater acceleration is evidenced by the greater rate of change of the slope of the graph for Planet Y.