A Boy Launches a Dart Horizontally by a Spring Gun
Average Horizontal Force Applied by the Spring
Final answer:
To find the average horizontal force applied by the spring, we can use the principles of projectile motion. Since the dart is launched horizontally, the initial vertical velocity is 0 m/s. In this case, m = 0.02 kg and v = 5 m/s, so F = (0.02 * 5) / 3 = 0.033 N.
Explanation:
To find the average horizontal force applied by the spring, we can use the principles of projectile motion. Since the dart is launched horizontally, the initial vertical velocity is 0 m/s. We can use the equation h = (1/2)gt^2 to find the time of flight, where h is the vertical displacement and g is the acceleration due to gravity. In this case, h = 45 m, so t = sqrt((2h)/g) = sqrt((2 * 45) / 9.8) = 3 s.
Next, we can find the initial horizontal velocity using the equation x = vt, where x is the horizontal displacement and v is the velocity. In this case, x = 15 m and t = 3 s, so v = x/t = 15/3 = 5 m/s.
Finally, we can find the average horizontal force by using the equation F = mv/t, where F is the force, m is the mass, v is the velocity, and t is the time. In this case, m = 0.02 kg and v = 5 m/s, so F = (0.02 * 5) / 3 = 0.033 N.
AboyHorizontal123 Final answer:To calculate the average horizontal force applied by the spring, use the formula for potential energy and the equation for projectile motion. Substitute the values and solve for the average horizontal force. Explanation:To calculate the average horizontal force applied by the spring, we need to consider the conservation of energy. The potential energy stored in the spring when it is compressed equals the kinetic energy of the dart when it is launched. We can use the formula for potential energy: PE = (1/2)kx^2 Where PE is the potential energy, k is the force constant of the spring, and x is the initial compression of the spring. Since the length of the gun's barrel is 10 cm and the dart lands 15 m away, we can use the equation for projectile motion to find the initial compression:d = (1/2)gt^2 Where d is the horizontal distance, g is the acceleration due to gravity, and t is the time of flight. From this equation, we can solve for t:t = sqrt(2d/g) Now we can substitute t into the equation for potential energy and solve for x:x = sqrt((2PE)/k) Finally, we can calculate the average horizontal force applied by the spring using:F_average = (1/2)m(v_x^2)/x Where F_average is the average horizontal force, m is the mass of the dart, and v_x is the horizontal velocity of the dart. Plugging in the given values, we get the answer.