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- Problems 67. 70. 71. and 72 are grouped. A A block of mass M is placed on a frictionless plane. The plane is inclined at an angle , and the block is a distance d from its end. Of course, we would expect the block to slip down the plane. Suppose we revolve the incline around the vertical axis shown in Figure P6.67 instead. At what period of revolution will the block remain in place on the plane? FIGURE P6.67 Problems 67. 71. and 72.A skier starts at rest at the top of a large hemispherical hill (Fig. P7.63). Neglecting friction, show that the skier will leave the hill and become airborne at a distance h = R/3 below the top of the hill. Hint: At this point, the normal force goes to zero. Figure P7.63An apple of mass 0.10 kg falls from a tree to the ground 2.00m below.a) How long does it take the apple to hit the ground?b) During the fall, what magnitude of force does the apple exert on the Earth?c) Using the force from b) and taking the Earth mass to be 6 × 1024kg, ap-proximately how far does the Earth move towards the apple during thetime it takes the apple to hit the ground?d) During the fall, is the apple moving, the Earth moving, or both, or neither?Explain your answer.e) In the real world, is the force exerted by the apple on the Earth of exactlythe same magnitude as the force exerted by the Earth on the apple
- A particle of mass m is projected vertically downwards in a medium which exerts a resistive force of magnitude kv2 per unit mass, where v is the speed of the particle and k is a positive constant given that 2u is theoritical maximum speed of the particle as it falls i)Show that k=g/4u2 The particle is now projected vertically upwards with speed u in the same medium ii)Find the greatest height reached by the particle above its point of projectionA 4.0-kg object is moving with speed 2.0 m/s. A 1.0-kg object is moving with speed 4.0 m/s. Both are stopped by the same amount of constant force. Which object travels the greater distance before stopping? a.the 1.0-kg object b.Both objects travel the same distance. c.the 4.0-kg object d.It is impossible to know without knowing how long each force acts.In an amusement park water slide, people slide down an essentially frictionless tube. The top of the slide is 3.0 m above the bottom where they exit the slide, moving horizontally, 1.2 m above a swimming pool. What horizontal distance do they travel from the exit point before hitting the water? Does the mass of the person make any difference?
- An object starts from rest at the origin and moves along the x axis subject to the force shown in the figure below. If the mass of the object is 37.0 kg, determine the speed of the object at the following positions. Each unit along the position axis is 2.00 m and each unit along the force axis is 3.00 N. (a) x = A (b) x = B (c) x = CA 1100-kg car coasts on a horizontal roadwith a speed of 19 m>s. After crossing an unpaved, sandy stretchof road 32 m long, its speed decreases to 12 m>s. (a) Was the network done on the car positive, negative, or zero? Explain. (b) Findthe magnitude of the average net force on the car in the sandysection.A 10-kg box initially at rest is pulled to the right along a frictionless horizontal surface by a horizontal force of 60N, determine the speed of the box after it has moved 2.0 m.
- Can you solve this question quickly please?The magnitude of the net force exerted in the negative x direction on a 9.6kg9.6kg particle varies in time as shown in the Figure below. If initially the velocity of the particle is +4.8m/s+4.8m/s along the x axis, determine the final velocity of the particle after the 5.0s5.0s interval. Please note that (+)(+) and (−)(−) signs are used to denote positive and negative directions along the xx axis! Don't forget to use the correct sign in your answer. Express your answer in units of m/sm/s using one decimal place.A high-diver of mass 70 kg jumps off a board 20 m above the water. If, 1.5 s after entering the water his downward motion is stopped, what average net force exerted on the diver? Choose A. 800 N B. 924 N C. 653 N D. No answer is correct.The IKAROS spacecraft, launched in 2010, was designed to test the feasibility of solar sails for spacecraft propulsion. These large, ultralight sails are pushed on by the force of light from the sun, so the spacecraft doesn’t need to carry any fuel. The force on IKAROS’s sails was measured to be 1.12 mN. If this were the only force acting on the 290 kg spacecraft, by how much would its speed increase after 6 months of flight?