An object with a mass of 3.4 kg is originally at rest on a horizontal, frictionless surface frictionless which is at the top of a frictionless incline with a length of 6 meters which is inclined at 28.9 degrees. Someone's hand applies a force to the object over some displacement and the object travels down the incline, across a horizontal frictionless surface and then up another frictionless incline which is inclined at 69.3 degrees. It travels 16 meters up the second incline before it stops. How much energy was given to the object from the person's hand in Joules?
E+PE1 =PE2
E=PE2-PE1=m•g•h2 -m•g•h1 =
=m•g•s2•sinβ- m•g•s1•sinα =
=m•g•( s2•sinβ -s1•sinα )=
=3.5•9.8•(16•sin69.3 - 6•sin28.9) =402 J
To find the energy given to the object by the person's hand, we need to calculate the work done on the object.
1. Calculate the gravitational potential energy lost by the object as it travels down the first incline.
- The formula for gravitational potential energy is: PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
- The height h can be calculated using trigonometry. The height of the incline (h1) is given by h1 = L * sin(theta1), where L is the length of the incline and theta1 is the angle of the incline.
- Substitute the values and calculate the gravitational potential energy lost, PE1.
2. Calculate the work done by the person's hand on the horizontal surface.
- Since the surface is frictionless, the work done is equal to the change in kinetic energy.
- The initial kinetic energy of the object is zero as it is at rest.
- The final kinetic energy can be calculated using the formula: KE = (1/2)mv^2, where m is the mass of the object and v is the velocity.
- Since the object starts from rest and ends at rest, the final kinetic energy is also zero.
- Therefore, the work done by the person's hand on the horizontal surface is zero.
3. Calculate the gravitational potential energy gained by the object as it travels up the second incline.
- Similar to step 1, calculate the height of the second incline, h2, using the formula: h2 = L * sin(theta2), where theta2 is the angle of the second incline.
- Calculate the gravitational potential energy gained, PE2, using the formula mentioned in step 1.
4. The total work done on the object is the sum of the gravitational potential energy lost (PE1) and gained (PE2).
- Total work done = PE1 + PE2
Remember to use consistent units in all calculations.
Finally, the energy given to the object by the person's hand is equal to the total work done on the object.