1- The initial velocity of the block in position A is 30 m/s. Knowing that the coefficient of kinetic friction between the block and the plane is uk = 0.30, determine the time it takes for the block to reach B with zero velocity. v = 0 В VA A Answer: t = 4.9s
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- A constant force of ''F'' acts on a mass as shown. The mass starts its motion from rest at position 1, the unstretched length of the spring is 250 mm, and the spring modulus is k=1,5 k?/m. Neglecting the friction, determine the required force ''F'' to cause the 2−kg mass to have a speed of v2=1,5 m/s at position 2.1- The roller coaster car has a brake and return system that has characteristics of a spring with a constant 45 lbs / ft. If the car has an initial velocity of 3 ft / s, determine the total force that the brake and return system must store. Assume that there is no friction, that the travel on the flat (from D to the spring) is 350 feet, and that the test weight of the car with passengers is 1000 Ibs. What does the sign of the answer mean? r=240 ft 90 ft RESORTE 60 ft2. A 40 kg block is at rest on the slope when a force F is applied to it. Determine the magnitude of F if the velocity of the block reaches 5 m/s when time t=2s. The coefficients of static and dynamic friction between the block and slope are 0.25 and 0.2, respectively. TTI S 4 F 3 TIT
- Using a forked rod, a smooth cylinder P, having a mass of 0.4 kg, is forced to move along the vertical slotted path r- (0.60) m, where e is in radians. If the cylinder has a constant speed of te- 2 m/s, determine the force of the rod and the normal force of the slot on the cylinder at the instant e- rad. Assume the cylinder is in contact with only one edge of the rod and slot at any instant. Hint To obtain the time derivatives necessary to compute the cylinder's acceleration components a, and a, take the first and second time derivatives of r- 0.60. Then, for further information, use Eq. 12-26 to determine 8. Also, take the time derivative of Eq. 12-26, noting that te - 0, to determine 8. -060Packages having a mass of 4-kg are delivered from a conveyor to a ramp with a velocity of v = 0.8 m/s. What is the velocity in which the packages will leave the ramp (at point B)? Consider e =30° andh = 12 m. The coefficient of the kinetic friction between the package and the ramp is = 0.35 Note. Please write your final answer in m/s in the provided box. Report your answer in 2 decimal places. For example: 2.34 m/s 0.8 m/sIn the position shown, block A is moving to the left at a speed of 9 m/s, and the spring is undeformed. Determine the stiffness of the spring k, in N/m, that would cause the system to stop after A has displaced 0.8 m. The coefficient of kinetic friction between block A and the horizontal surface is 0.25, and the weights on the pulleys are negligible. The mass of block A is 3.0 kg, and the mass of block B is 5.5 kg. k 0000000000 VA A Мек B
- 2. A force is applied to block A at angle of 40 degrees with the horizontal. Determine the friction force and the acceleration of block A in the system below if the coefficient of friction between A and the surface is 0.4. (Normal Force, N = 450N) Sign convention 15N 250 kg A B 75 kgThe coefficient of kinetic friction between the m = 10.4 kg crate and the plane is u = 0.3. Initially, the crate is at the position 1 on the horizontal plane with a velocity v, = 14.8 m/s. The crate moves a distance D = 4 m before going upward on the incline plane that has an angle with the horizontal of e = 35 degrees. The initial state and the state at the bottom of the incline plane are at h = 0 m. Determine the distance L the crate will travel upward where it will be at rest. g = 9.81 m/s?. h Position 1 13.626 m O 12.161 m O 15.091 m O 10.052 mQuestion a) The 10-kg block has a speed of 4 m/s when the force of F = (8t²) N is applied (Figure Q2(a)). Determine the velocity of the block at t = 10 s. The coefficient of kinetic friction at the surface is μk = 0.2. F = (81²) N v = 4 m/s Figure Q2(a) b) The force of F = 50 N is applied to the cord when s = 2 m as shown in Figure Q2(b). If the 6-kg collar is originally at rest, determine its velocity at s = 0. Neglect friction. 1.5 m F Figure Q2(b) A
- The 130-kg crate shown is on a smooth horizontal plane and has an initial velocity of 3 m/s. A towing force of 200 N is applied at an angle of 45° for 5 s. Determine the final velocity (m/s) after 5 s. oopo 45° 200 N Hint: From the derivation F=ma, it requires same line of action (or at the same axis).Q5) The 50-kg crate shown rests on a rough horizontal surface for which the coefficient of kinetic friction is #x=0.3. An electrically powered winch is utilized to accelerate the crate at a constant rate until it attains a speed of v-Sm's within a distance of s=20m. If the motor and the winch have an efficiency of n-0.70, determine the power that must be supplied to the motor when s= 20 m. 20 m 50 kg D2. The block (A) has a mass of 10 kg and the coefficient of dynamic friction between the block and the ground is μ = 0.3. Block B has a mass of 15 kg and slides down a frictionless pole. If the blocks start from at x=0 calculate: a. The distance block A moves after block B has fallen 4 m b. The relationship between the speed of A and the speed of B c. The work done by friction on block A d. The velocity of block B. B 2m A