Question

A 0.8 kg mass is held against a spring of stiffness k = 56 N/m compressing it by a distance d m as shown. When released from rest it slides along the horizontal surface and first encounters a rough patch of length L = 0.4 m with coefficient of kinetic friction ?k = 0.25. Then, at point P as shown, the mass encounters a smooth, circular vertical path of radius R = 0.8 m. Take g = 10 m/s^2. a) [4] If ? 'theta' denotes the angle as shown, determine the exact speed v of the mass along the circular part of the path as a function of the angle ?, the initial compression of the spring d, and the numbers given. [Your answer may use only the symbols d, ? 'theta', and integers. Hint: write a single energy equation applied between the initial release point and an arbitrary final point along the circular part of the path. 10 tries for this part, i.e. 10% deduction for each incorrect attempt.] v(d, ?) = m/s b) [2] What is the exact magnitude of the normal force the circular part of the path applies on the mass, again as a function of ?, d and the given numbers? (Your answer can only depend on the symbols ? and d and your numbers will be integers.) N(d, ?) = N c) [1] What is the minimum amount the spring must be compressed, dmin, so that the mass makes it all the way around the vertical circular path without losing contact? (Express your answer correctly to three sig digs.) dmin = m

          A 0.8 kg mass is held against a spring of stiffness k = 56 N/m compressing it by a distance d m as shown. When released from rest it slides along the horizontal surface and first encounters a rough patch of length L = 0.4 m with coefficient of kinetic friction ?k = 0.25. Then, at point P as shown, the mass encounters a smooth, circular vertical path of radius R = 0.8 m.

Take g = 10 m/s^2.

a) [4] If ? 'theta' denotes the angle as shown, determine the exact speed v of the mass along the circular part of the path as a function of the angle ?, the initial compression of the spring d, and the numbers given.

[Your answer may use only the symbols d, ? 'theta', and integers. Hint: write a single energy equation applied between the initial release point and an arbitrary final point along the circular part of the path. 10 tries for this part, i.e. 10% deduction for each incorrect attempt.]
v(d, ?) = m/s

b) [2] What is the exact magnitude of the normal force the circular part of the path applies on the mass, again as a function of ?, d and the given numbers?
(Your answer can only depend on the symbols ? and d and your numbers will be integers.)
N(d, ?) = N

c) [1] What is the minimum amount the spring must be compressed, dmin, so that the mass makes it all the way around the vertical circular path without losing contact? (Express your answer correctly to three sig digs.)
dmin = m

A 0.8 kg mass is held against a spring of stiffness k = 56 N/m compressing it by a distance d m as shown. When released from rest it slides along the horizontal surface and first encounters a rough patch of length L = 0.4 m with coefficient of kinetic friction ?k = 0.25. Then, at point P as shown, the mass encounters a smooth, circular vertical path of radius R = 0.8 m.

Take g = 10 m/s^2.

a) [4] If ? 'theta' denotes the angle as shown, determine the exact speed v of the mass along the circular part of the path as a function of the angle ?, the initial compression of the spring d, and the numbers given.

[Your answer may use only the symbols d, ? 'theta', and integers. Hint: write a single energy equation applied between the initial release point and an arbitrary final point along the circular part of the path. 10 tries for this part, i.e. 10% deduction for each incorrect attempt.]
v(d, ?) = m/s

b) [2] What is the exact magnitude of the normal force the circular part of the path applies on the mass, again as a function of ?, d and the given numbers?
(Your answer can only depend on the symbols ? and d and your numbers will be integers.)
N(d, ?) = N

c) [1] What is the minimum amount the spring must be compressed, dmin, so that the mass makes it all the way around the vertical circular path without losing contact? (Express your answer correctly to three sig digs.)
dmin = m

Added by Asunci-N P.

Question

Please give Ace some feedback