Using \( \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2} \), find the weight of a 4 kg object. An object weighs 350 N . Find its max Use \( \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2} \). If 100 kg person weighed 400 N on the planet Zorg, what is the acceleration due to gravity on Zorg? A sled is pushed with 30 N and sliding friction is 10 N. Find the net force on the sled. Two boys push on a box with 3 N and 6 N to the right. The net force is 7 N . Find the force of friction. A car's engine pushes with 45 N to the right. If it is at equilibrium, how much air friction is there and what is the car's acceleration? A 2 mig object accelerates at \( 5 \mathrm{~m} / \mathrm{s}^{2} \). Find the force. A boat's motor pushes with 25 N of force and viscous. friction resists with 5 N . If the boat is 100 kg , find its acceleration.
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To find the weight of a 4 kg object, you multiply its mass by the acceleration due to gravity: \( \text{Weight} = \text{mass} \times g = 4 \, \text{kg} \times 10 \, \text{m/s}^2 = 40 \, \text{N} \). For the object weighing 350 N, its mass can be found using \( \text{mass} = \frac{\text{weight}}{g} = \frac{350 \, \text{N}}{10 \, \text{m/s}^2} = 35 \, \text{kg} \). To find the gravity on Zorg, use the formula \( g = \frac{W}{m} \). A 100 kg person weighs 400 N, thus the gravity is \( g = \frac{400 \, \text{N}}{100 \, \text{kg}} = 4 \, \text{m/s}^2 \) on Zorg. For the sled with a push of 30 N and friction of 10 N, the net force can be computed as \( \text{Net Force} = \text{Applied Force} - \text{Friction} = 30 \, \text{N} - 10 \, \text{N} = 20 \, \text{N} \) to the right. When two boys push a box with forces of 3 N and 6 N to the right, the net force is 7 N. Therefore, the force of friction is \( \text{Friction} = \text{Total Push} - \text{Net Force} = (3 \, \text{N} + 6 \, \text{N}) - 7 \, \text{N} = 2 \, \text{N} \). In equilibrium, the car's engine pushes with 45 N. Thus, air friction must be equal to the push: \( \text{Air Friction} = 45 \, \text{N} \). Since it’s at equilibrium, the acceleration is \( 0 \, \text{m/s}^2 \). For the 2 mg object accelerating at \( 5 \, \text{m/s}^2 \), convert the mass to kg: \( 2 \, \text{mg} = 0.002 \, \text{kg} \). Then calculate force: \( F = m \times a = 0.002 \, \text{kg} \times 5 \, \text{m/s}^2 = 0.01 \, \text{N} \). Lastly, for the boat with a 25 N motor force and 5 N friction, the net force is \( 25 \, \text{N} - 5 \, \text{N} = 20 \, \text{N} \). To find the acceleration, use \( a = \frac{\text{Net Force}}{m} = \frac{20 \, \text{N}}{100 \, \text{kg}} = 0.2 \, \text{m/s}^2 \).
