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What is the frequency of an acrobat swinging on a trapeze if the cables are approximately 2.5 m long?
A 15g bullet traveling at 500m/s strikes an 0.8kg block of wood that is balanced on the table edge 0.8m above the ground. If the bullet buries itself in the block . Find the distance D at wich the block hits the floor.
A 2kg block is released 4m from a massless spring with a force constant K=100N/m that is aong a plane inlined at 30°. If the coefficient of kinetic friction between the plane and the block is 0.2, find the maximum compression.
Two vehicles are approaching an intersection. One is a 2500-kg pick up travelling at 14.0 m/s from east to west ( the -x direction), and the other is a 1500-kg sedan going from north to south ( the + y direction) at 23.0 m/s. What is the x components of the net momentum for this system?
A person is jumping from a height ℎ0 = 10 m with zero initial velocity and a cricket ball is thrown directly upward with an initial velocity 𝑣𝑣0 = 9.8 m/s at the same instant when time t = 0 s as shown in Fig. 1. Consider h = 11.5 m and 𝚤𝚤̂and 𝚥𝚥̂ to be the unit vectors along the X and Y axis. Gravity is acting along the -𝚥𝚥̂direction and the magnitude of gravitational acceleration is given by g = 9.81 m/s2 . The red dot on the person represents his center of mass. (a) (4 marks) If the person and the cricket ball consist of a system, find the position and velocity of the center of mass of the system at time t = 0.5 s.
(b) (2 marks) If it takes 0.01 seconds for the person to come to complete rest when he hits the ground, calculate the average force acting on the person.
(c) (4 marks) Now consider when the person hits the ground, he bends his knees such that the center of mass of his body is lowered by 15 cm. If the maximum force that the bone of his legs can withstand is 50000 N, will he break his legs?
A figure skater is spinning at an angular velocity of 8.0 rad/s. Assume that her moment of inertia is 80 kg/m2.
a. What is the angular momentum of the figure skater?
b. How much torque is required to slow her down to a stop in 5.0 seconds?
3.1 An aluminium tin is filled to the brim with a liquid. The tin’s initial volume at 5.00 °C is 3.5 10−4 m3. The coefficient of volume expansion for aluminium is 69.0 10−6 (C°)−1. When the tin and the liquid are heated to 78.0 °C, 3.6 10−6 m3 of liquid spills over. Calculate the coefficient of volume expansion of the liquid. [HINT: The tin and the liquid are heated so their temperatures change by the same amount.]
Calculate the force of gravity of the husband and wife, the husband has a mass of 85kg and the wife has a mass of 60kg. They are 0.75m apart.
A 2kg block is released 4m from a massless spring with a force constant K=100N/m that is aong a plane inlined at 30°. if the plane is frictionless , find the maximum compression of the spring.
A crate of mass 10kg is pulled up arough incline with an initial speed of 1.5m/s. the pulling force is 100N parallel to the incline which makes an angle of 30° with the horizontal. the coefficient of kinetic friction is 0.4 and the crate is pulled 5m. How much mechanical energy is lost due to friction?
