A 500 N force is applied to an object accelerating at 25 m/s^2. what is the mass of the object?
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The box has 3 forces acting on it:
• its own weight (magnitude <em>w</em>, pointing downward)
• the normal force of the incline on the box (mag. <em>n</em>, pointing upward perpendicular to the incline)
• friction (mag. <em>f</em>, opposing the box's slide down the incline and parallel to the incline)
Decompose each force into components acting parallel or perpendicular to the incline. (Consult the attached free body diagram.) The normal and friction forces are ready to be used, so that just leaves the weight. If we take the direction in which the box is sliding to be the positive parallel direction, then by Newton's second law, we have
• net parallel force:
∑ <em>F</em> = -<em>f</em> + <em>w</em> sin(35°) = <em>m a</em>
• net perpendicular force:
∑<em> F</em> = <em>n</em> - <em>w</em> cos(35°) = 0
Solve the net perpendicular force equation for the normal force:
<em>n</em> = <em>w</em> cos(35°)
<em>n</em> = (15 kg) (9.8 m/s²) cos(35°)
<em>n</em> ≈ 120 N
Solve for the mag. of friction:
<em>f</em> = <em>µ</em> <em>n</em>
<em>f</em> = 0.25 (120 N)
<em>f</em> ≈ 30 N
Solve the net parallel force equation for the acceleration:
-30 N + (15 kg) (9.8 m/s²) sin(35°) = (15 kg) <em>a</em>
<em>a</em> ≈ (54.3157 N) / (15 kg)
<em>a</em> ≈ 3.6 m/s²
Now solve for the block's speed <em>v</em> given that it starts at rest, with <em>v</em>₀ = 0, and slides down the incline a distance of ∆<em>x</em> = 3 m:
<em>v</em>² - <em>v</em>₀² = 2 <em>a</em> ∆<em>x</em>
<em>v</em>² = 2 (3.6 m/s²) (3 m)
<em>v</em> = √(21.7263 m²/s²)
<em>v</em> ≈ 4.7 m/s
Explanation:
1. study of conversion of heat to mechanics → thermodynamics
A branch of physical science which deals with heat and other forms of energy.
2. The Law of Conservation of Energy → first Law of Thermodynamics
Energy cannot be created nor be destroyed. According to first law of thermodynamics total energy of the system is always constant.
3. Result of applied energy → work
Work is the way of system to release its energy.
4. Principle that states that in any energy transformation some energy is dissipated as heat → Second Law of Thermodynamics
5. energy of motion → kinetic energy
Kinetic energy is defined as energy possessed by the body due to its motion.
6. work/displacement → force
Work is product of force and displacement.
7. power · time → energy
Power is defined energy per unit time.
8. Device that transforms heat energy into mechanical energy → heat engine
heat engine is a device which converts the heat energy which is released due to combustion of fuel into a useful work that is mechanical energy.
9 . Energy due to position → potential energy
Potential energy is defined as energy possessed by the body due to its position.
10. efficiency of a heat engine unit of heat → calorie
11. Measure of molecular motion → Temperature
Kinetic energy is directly proportional to temperature.
Greater the motion more will be the kinetic energy and with more will be the temperature.
12. Heat given off by a liquid with no change in temperature → latent heat of fusion
Latent heat of fusion is defined as heat released by 1 mole of substance when it under goes phase change that is from solid to liquid.
13. Motion within solids → vibrational motion
Vibrational motion is the motion in which particle oscillates from its mean position.
14. Phase of matter on the sun → plasma
Plasma is hot ionized gas with equal number of positive and negative ions. Due to high temperature of sun most the gas are in the plasma state.