A block of mass m = 5.66 kg slides down from an inclined frictionless ramp that forms an angle θ = 17.80∘ with the ground. A long spring with a relaxed length s0 = 1.69 m and a spring constant k = 575.83 N/m is situated at the base of the ramp. The block slides down with a velocity of v = 6.90 m/s and it compressed the spring to a length of s = 0.95 m. What is the distance the block travels from the top of the ramp to the tip of the spring? Round your answer to 2 decimal places. after
A block of mass m = 4.70 kg slides down from an inclined frictionless ramp that forms an angle θ = 36.19∘ with the ground. A long spring with a relaxed length s0 = 0.65 m is situated at the base of the ramp. The block started at a distance d = 2.11 m from the tip of the relaxed spring, with an initial velocity v = 4.23 m/s down the ramp. It compressed the spring to a length of s = 0.19 mbefore temporarily coming to a stop. What is the spring constant of the spring? Round your answer to 2 decimal places.
A boy sits on a sled at the top of a snowy hill of length L = 85 m. The boy and sled have a combined mass of 40 kg, and the hill makes an angle of θ = 21 degrees above the horizontal. The boy and sled slide down the snowy hill without friction. a. (2 points) Draw the free body diagram of all the forces acting on the boy. b. (3 points) Use Newton's second law to find the acceleration of the boy and sled at the bottom of the hill. c. (3 points) Use kinematics to calculate the velocity of the boy and sled at the bottom of the hill. You may assume that the boy and sled started from rest.
An elevator car has two equal masses attached to the ceiling as shown. (Assume m = 3.30 kg.) (a) The elevator ascends with an acceleration of magnitude 1.20 m/s2. What are the tensions in the two strings? (Enter your answers in N.) T1 = N T2 = N (b) The maximum tension the strings can withstand is 77.7 N. What is the maximum acceleration of the elevator so that a string does not break? (Enter the magnitude in m/s2.) m/s2
Example 1. Person A is trying to keep his balance while on a sled B that is sliding down an icy incline. Letting mA = 78 kg and mB = 25 kg be the masses of A and B respectively, and assuming that there is enough friction between A and B for A not to slide with respect to B, determine the value of the normal reaction force between A and B as well as the magnitude of their acceleration if θ = 20∘. Friction between the sled and the incline is negligible.
Two blocks of mass M1 and M2 are connected by a massless string that passes over a massless pulley as shown in the figure. M1 has a mass of 2.25 kg and rests on an incline of θ1 = 75.5∘. M2 rests on an incline of θ2 = 35.5∘. Find the mass of block M2 so that the system is in equilibrium (i. e., not accelerating). All surfaces are frictionless. M2 = kg Figure is not to scale.
The figure shows a thin plastic rod of length L = 14.4 cm and uniform charge 78.2 fC. (a) In terms of distance d, charge density λ and ε0 find an expression for the electric potential at point P1. Next, substitute variable x for d and find an expression for the magnitude of the component Ex of the electric field at P1 (in terms of d and other variables). (b) What is the direction of Ex relative to the positive direction of the x axis? (c) What is the value of Ex at P1 for x = d = 8.35 cm? (d) From the symmetry in figure determine Ey at P1.
A 34 kg body is moving through space in the positive direction of an x axis with a speed of 120 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 14 kg, moves away from the point of explosion with a speed of 140 m/s in the positive y direction. A second part, with a mass of 10 kg, moves in the negative x direction with a speed of 430 m/s. What are the (a) x-component and (b) y-component of the velocity of the third part? (c) How much energy is released in the explosion? Ignore effects due to the gravitational force. (a) Number Units (b) Number Units (c) Number Units