Homework SourseA force F 6i 2jN acts on a particle that undergoes displac
A force F = (6i - 2j)N acts on a particle that undergoes displacement d = (3i + 5j)m. Find a the work done by the force on the particle and the angle between F and d. Hooke\'s law and work done by a spring. If it takes 4.000 J to stretch a spring 10.0 cm from its unstretched lengths, determine the extra work required to stretch it an additional 10.0 cm. Also calculate the force that is required to hold the spring in both positions. Work-energy theorem and work done by non-conservative forces. A horizontal frictionless spring/mass system with a spring constant of k = 100 N/m is stretch 15.0 cm from its equilibrium position. Find: The initial potential energy of the spring. Work required to stretch the spring to that initial position. If the spring is then released, find the speed with which the mass passes through the equilibrium position. Take mass to be m = 0.500 kg. A block having a mass of 0 800 kg is given an initial velocity V_1 = 1.25 m/s to the right. It collides head on with a horizontal spring of negligible mass and force constant k = 50 N/m, resting on the table. Assuming the surface to be frictionless, calculate the maximum compressors of the spring after the collision. Assume that the block gets stuck to the spring. Suppose a constant force of kinetic friction acts between the block and the surface, with mu_t = 0.500. If the speed of the block at the moment it collides with the spring is V_A = 1.25 m/s, what is the maximum compression of the spring? A 2000 kg car starts from rest and coasts down from the top of a 5.00 m-long driveway that is sloped at an angle of 200 degree with the horizontal. If an average friction force of 4000 N impedes the motion of the car, find the speed of the car at the bottom of the driveway.
Solution
1.
The force is given by,
F = 6 i - 2 j
the displacement is,
d = 3 i + 5 j
hence, the work done is,
W = F.d = [6 i - 2 j] . [ 3 i + 5 j]
= 8 J
Angle between F and d is,
@ = cos-1[F.d / |F||d|]
= cos-1[8 / [sqrt(6^2+2^2)]*[sqrt(3^2+5^2)]
= 77.47o
remaining questions post seperately.
