A particle of mass 4.0 kg is constrained to move along the x-axis under a single force F(x) = -cx³, where c = 8.0 N/m³. The particle's speed at A, where x₁ = 1.0m, is 6.0 m/s. What is its speed at B, where x = -2.0m?
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- A particle of mass 4.0 kg moves under the influence of the force F(x) = (-5x + 7x) N. If its speed at x = -2.4 m is v = 24.0 m/s, what is its speed (in m/s) at x = 2.4 m? m/sa girl and her bicycle have a total mass of 60kg. at the top of the hill her speed is 5.0m/s. The hill is 5.0 m high and 100 m long. If the force of friction as she rides down the hill is 20N, what is her speed at the bottom?A particle of mass 18.8 kg moves along the x-axis with a potential energy U whose dependence on position x is shown in the figure. If the total mechanical energy E of the particle is 110 J, what is the speed in m/s of the particle at 7 m? 15 U (J) 10 V. 5 4 8 10 X (m) 00 6. 20
- The potential energy of a particle as a function of position will be given as U(x) = A x2 + B x + C,where U will be in joules when x is in meters. A, B, and C are constants. What is the force on this particle, in newtons, at x+39cm, if the constants are A= 2.2 J/m^2 , B= 2.2 J/m, and C=6.5 J?1.A particle of mass 6-kg moves under the influence of the force F(x)=(4√x)F(x)=(4x) N. If its speed at x=2.0x=2.0 m is v=7v=7 m/s, what is its speed at x=7.0x=7.0 m? v = m/s 2. A 102-kg man is skiing across level ground at a speed of 14.5 m/s when he comes to the small slope 1.8 m higher than ground level shown in the following figure. If the skier coasts up the hill, what is his speed when he reaches the top plateau? Assume friction between the snow and skis is negligible.v=v= m/s What is his speed when he reaches the upper level if an 80-N frictional force acts on the skis?v=v= m/s29.A particle of mass 2.0 kg moves under the influence of the force F(x)=(−5x² +7x) N. If its speed at x=-4.0 m is v=20.0 m/s, what is its speed at x = 4.0 m? Solution 14 m/s
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- On board the starship Serenity, Captain Mal has two boxes connected together by a cord that passes over a massless, frictionless pulley mounted on the ceiling of the storage bay. The first box has a mass of 252.0kg and the second box has a mass of 278.0kg. If the 278.0kg box starts off at rest 2.60m above the ground, find the speed of the box when it reaches the ground. Assume the gravity on Serenity is 9.80m/s2.A particle of mass 2.0 kg moves under the influence of the force F(x) =(−5x2 + 7x)N. If its speed at x = −4.0 m is v = 20.0 m/s, what is its speed at x = 4.0 m?A 3.80 kg block is pulled up a frictionless inclined plane by a 53.0 N force that is parallel to the plane, starting from rest.The normal force on the block from the plane has magnitude 10.4 N.What is the block’s speed when its displacement up the ramp is 3.40 m?