Question
Blocks X and Y of masses 3.0 kg and 5.0 kg, respectively, are connected by a light string and are both on a level horizontal surface of negligible friction. A force F = 12 N is exerted on block Y, as shown in the figure above. What is the tension in the string connecting the two blocks?
(A) 1.5 N
(B) 4.0 N
(C) 4.5 N
(D) 7.5 N
(E) 12 N
Answer/Explanation
An object of mass 0.5 kg is given an initial velocity and then slides across a horizontal surface. The object experiences a resistive force that is a function of velocity. The velocity v of the object as a function of time t is given by \(v(t)=\alpha e^{-\beta t}\)=,where\( \alpha =2m/s\) and\( \beta =3s^{-1}\).
Question
Which of the following is a correct expression for the net force, in newtons, exerted on the object as a function of time?
(A)\(6e^{-3t}\)
(B)\(-3e^{-3t}\)
(C)\(e^{-3t}\)
(D)\(2e^{-3t}\)
(E)\(\frac{2}{3\left ( 1-e^{-3t} \right )}\)
Answer/Explanation
Ans:B
The acceleration is the derivative of the velocity, \(a=\frac{dv}{dt}=\frac{dv}{t}(\alpha e^{\beta t})=-\beta \alpha e^{-\beta t}\)Substituting into an equation for
Newton’s second law yields
\(F_{net}=ma=m-\beta \alpha e^{-\beta t}\)
Question
Two blocks rest on a table, as shown above. The bottom block is pulled to the right by an applied force \(\vec{F}\) F that is strong enough so that the two blocks do not move together (i.e., they do not have the same acceleration or velocity). There is friction between the blocks, but the tabletop is frictionless. When the top block leaves the bottom block, where does it land and why?
(A) The top block will land directly below where it starts because objects at rest tend to stay at rest.
(B) The top block will land to the left of where it starts because of the static friction between the blocks.
(C) The top block will land to the left of where it starts because of the kinetic friction between the blocks.
(D) The top block will land to the right of where it starts because of the static friction between the blocks.
(E) The top block will land to the right of where it starts because of the kinetic friction between the blocks.
Answer/Explanation
Ans:E
Question
A sphere of mass m is dropped from the top of a building and reaches the ground before achieving terminal velocity. The force of air resistance that acts on the sphere as it falls is given by \(F = −kv\) , where k is a positive constant and v is the velocity of the sphere. What happens to the magnitude of the sphere’s velocity and acceleration, and to the distance it falls during each second, as the sphere approaches the ground?
Magnitude of Velocity Magnitude of Acceleration Distance of Fall Each Second
(A) Increases Increases Increases
(B) Increases Decreases Increases
(C) Increases Decreases Decreases
(D) Decreases Increases Decreases
(E) Decreases Decreases Increases
Answer/Explanation
Ans:B
Question
A 3.0 kg block accelerates at \(2.0 m /s^2\) because of a constant net force. A block of unknown mass accelerates at\( 6.0 m s^2\) because of the same net force. What is the mass of the second block?
(A) 9.0 kg
(B) 4.0 kg
(C) 3.0 kg
(D) 1.5 kg
(E) 1.0 kg