Students investigating the motion of golf balls in a medium perform two experiments where golf balls are introduced into different media. In the first experiment, the balls are dropped vertically downward into a tank of water. In the second experiment, the balls are compressed against an ideal spring and then propelled horizontally into a tube filled with air, as shown in the figure below. As the golf ball moves through a medium, it experiences a drag force FD that opposes its motion, as described by the equation:FD=12CDρAv2𝐹D=12𝐶D𝜌𝐴𝑣2where CD is the drag coefficient, ρ is the medium's density, A is the cross-sectional area of the ball, and v is the velocity of the ball. Question 43The students compress a 40 g golf ball a distance of 80 cm against a spring with spring constant k = 100 N/m. After it is released from the spring, what is the velocity of the ball as it enters the air-filled tube?A.40 m/sB.45 m/sC.56 m/sD.125 m/sSubmit
Question
Students investigating the motion of golf balls in a medium perform two experiments where golf balls are introduced into different media. In the first experiment, the balls are dropped vertically downward into a tank of water. In the second experiment, the balls are compressed against an ideal spring and then propelled horizontally into a tube filled with air, as shown in the figure below. As the golf ball moves through a medium, it experiences a drag force FD that opposes its motion, as described by the equation:FD=12CDρAv2𝐹D=12𝐶D𝜌𝐴𝑣2where CD is the drag coefficient, ρ is the medium's density, A is the cross-sectional area of the ball, and v is the velocity of the ball. Question 43The students compress a 40 g golf ball a distance of 80 cm against a spring with spring constant k = 100 N/m. After it is released from the spring, what is the velocity of the ball as it enters the air-filled tube?A.40 m/sB.45 m/sC.56 m/sD.125 m/sSubmit
Solution
To solve this problem, we need to use the principle of conservation of energy. The potential energy stored in the spring when it is compressed is converted into kinetic energy when the ball is released.
The potential energy (PE) stored in a spring is given by the formula:
PE = 1/2 * k * x^2
where k is the spring constant and x is the distance the spring is compressed.
Substituting the given values:
PE = 1/2 * 100 N/m * (0.8 m)^2 = 32 Joules
The kinetic energy (KE) of an object is given by the formula:
KE = 1/2 * m * v^2
where m is the mass of the object and v is its velocity.
We know that the potential energy in the spring is converted into kinetic energy in the ball, so we can set the two equal to each other and solve for v:
32 J = 1/2 * 0.04 kg * v^2
Solving for v gives:
v = sqrt((2 * 32 J) / 0.04 kg) = 40 m/s
So, the velocity of the ball as it enters the air-filled tube is 40 m/s. The answer is A. 40 m/s.
Similar Questions
A ball is projected in an environment where air resistance can be ignored.
A spherical solid ball of volume V is made of a material of density 1. It is falling through aliquid of density 2(2 < 1). Assume that the liquid applies a viscous force on the ball that isproportional to the square of its speed v, i.e. Fviscous = kv2(k > 0). The terminal speed of theball is:
A paper ball is released from rest, and goes on to fall through a large vertical distance. As it falls through the air, it is acted upon by two forces – air resistance and its weight. Which of the following correctly describes its motion after it is dropped?It will accelerate at an increasing rate and then reach its terminal velocityIt will accelerate uniformly before reaching its terminal velocityIt will accelerate uniformlyIt will accelerate at a decreasing rate and then reach its terminal velocity
Ignoring air resistance, after being dropped the vertical velocity of a ball immediately before contacting a surface is dependent on: Question 18Answera.the height from which the ball was dropped and gravityb.the height from which the ball was dropped, gravity and the surface texture of the ballc.the height from which the ball was dropped, gravity, the mass of the ball, and surface texture of the balld.the height from which the ball was dropped, the mass of the ball, and surface texture of the balle.the influence of gravity, the mass of the ball and surface texture of the ball
A golf ball is on a tee. It is hit with a golf club. The ball flies through the air. Which type of force caused the motion of the ball? A. friction B. push C. pull D. gravityReset
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.